arXiv subjects

Michele Trenti

Publications and source records attributed to Michele Trenti.

At least 109 records · Page 6Linked to original sources

arXiv2019

Constraining the neutral fraction of hydrogen in the IGM at redshift 7.5

We present a large spectroscopic campaign with Keck/MOSFIRE targeting Lyman-alpha emission (Ly$α$) from intrinsically faint Lyman-break Galaxies (LBGs) behind 12 efficient galaxy cluster lenses. Gravitational lensing allows us to probe the more abundant faint galaxy population to sensitive Ly$α$ equivalent width limits. During the campaign we targeted 70 LBG candidates with MOSFIRE Y-band, selected photometrically to cover Ly$α$ over the range $7 5$ emission lines in 2 of these galaxies and find that they are likely Ly$α$ at $z=7.148\pm0.001$ and $z=7.161\pm0.001$. We present new lens models for 4 of the galaxy clusters, using our previously published lens models for the remaining clusters to determine the magnification factors for the source galaxies. Using a Bayesian framework that employs large scale reionization simulations of the intergalactic medium (IGM) as well as realistic properties of the interstellar medium and circumgalactic medium, we infer the volume-averaged neutral hydrogen fraction, $\overline{x}_{\mathrm{HI}}$, in the IGM during reionization to be $\overline{x}_{\mathrm{HI}}=0.88^{+0.05}_{-0.10}$ at $z=7.6\pm0.6$. Our result is consistent with a late and rapid reionization scenario inferred by Planck.

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arXiv2018

Observational determination of the galaxy bias from cosmic variance with a random pointing survey: Clustering of z~2 galaxies from Hubble's BoRG survey

Gravitational clustering broadens the count-in-cells distribution of galaxies for surveys along uncorrelated (well-separated) lines of sight beyond Poisson noise. A number of methods have proposed to measure this excess "cosmic" variance to constrain the galaxy bias (i.e. the strength of clustering) independently of the two-point correlation function. Here we present an observational application of these methods using data from 141 uncorrelated fields (~700 arcmin$^2$ total) from Hubble's Brightest of Reionizing Galaxies (BoRG) survey. We use BoRG's broad-band imaging in optical and near infrared to identify N~1000 photometric candidates at z~2 through a combination of colour selection and photometric redshift determination, building a magnitude-limited sample with $m_{AB}\leq24.5$ in F160W. We detect a clear excess in the variance of the galaxy number counts distribution compared to Poisson expectations, from which we estimate a galaxy bias $b \approx 3.63 \pm 0.57$. When divided by SED-fit classification into ~400 early-type and ~600 late-type candidates, we estimate biases of $b_{early} \approx 4.06 \pm 0.67$ and $b_{late} \approx 2.98 \pm 0.98$ respectively. These estimates are consistent with previous measurements of the bias from the two-point correlation function, and demonstrate that with $N\gtrsim100$ sight-lines, each containing $N\gtrsim5$ objects, the counts-in-cell analysis provides a robust measurement of the bias. This implies that the method can be applied effectively to determine clustering properties (and characteristic dark-matter halo masses) of z~6-9 galaxies from a pure-parallel James Webb Space Telescope survey similar in design to Hubble's BoRG survey.

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arXiv2018

Mass and Light of Abell 370: A Strong and Weak Lensing Analysis

We present a new gravitational lens model of the Hubble Frontier Fields cluster Abell 370 ($z = 0.375$) using imaging and spectroscopy from Hubble Space Telescope and ground-based spectroscopy. We combine constraints from a catalog of 1344 weakly lensed galaxies and 39 multiply-imaged sources comprised of 114 multiple images, including a system of multiply-imaged candidates at $z=7.93 \pm 0.02$, to obtain a best-fit mass distribution using the cluster lens modeling code Strong and Weak Lensing United. As the only analysis of A370 using strong and weak lensing constraints from Hubble Frontier Fields data, our method provides an independent check on assumptions in other methods on the mass distribution. Convergence, shear, and magnification maps are made publicly available through the HFF website. We find that the model we produce is similar to models produced by other groups, with some exceptions due to the differences in lensing code methodology. In an effort to study how our total projected mass distribution traces light, we measure the stellar mass density distribution using Spitzer/Infrared Array Camera imaging. Comparing our total mass density to our stellar mass density in a radius of 0.3 Mpc, we find a mean projected stellar to total mass ratio of $\langle f* \rangle = 0.011 \pm 0.003$ (stat.) using the diet Salpeter initial mass function. This value is in general agreement with independent measurements of $\langle f* \rangle$ in clusters of similar total mass and redshift.

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arXiv2018

Near real-time telecommand solutions for CubeSats: State of the art and applications to the SkyHopper mission

Cubesats and similarly scaled nano-satellites present significant opportunities for hosting both scientific and commercial payloads for Earth sensing and astronomical observations, in particular in the area of rapid-response observations to external triggers. However, one limiting factor to full exploitation of the CubeSat potential in this area lies in the traditional approach of ground-spacecraft communications, which is based on infrequent contact via a limited network of ground stations. An alternative is to leverage existing commercial machine-to-machine orbital networks to transmit the triggers in near-real-time. Here, we present an analysis framework for calculating the likelihood of a time to first contact and the length of contact under minimum guaranteed conditions for these networks. The analysis is then extended to likely operational conditions in orbit, and the results of a comparative trade study of a number of orbital networks are presented, with an emphasis on the applicability to the SkyHopper Space Telescope CubeSat, a nanosatellite astronomical observatory currently undergoing preliminary design. It was found that near-real- time telecommands could be transmitted to SkyHopper within 10min with a likelihood of 62% using the Globalstar network, or a likelihood of 74% using the Iridium network, under predicted nominal operational conditions in orbit. Future networks currently under development could improve these figures to reach greater than 98% coverage with a one second latency.

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arXiv2018

RELICS: Strong Lensing analysis of the galaxy clusters Abell S295, Abell 697, MACS J0025.4-1222, and MACS J0159.8-0849

We present a strong-lensing analysis of four massive galaxy clusters imaged with the Hubble Space Telescope in the Reionization Lensing Cluster Survey. We use a Light-Traces-Mass technique to uncover sets of multiply images and constrain the mass distribution of the clusters. These mass models are the first published for Abell S295 and MACS J0159.8-0849, and are improvements over previous models for Abell 697 and MACS J0025.4-1222. Our analysis for MACS J0025.4-1222 and Abell S295 shows a bimodal mass distribution supporting the merger scenarios proposed for these clusters. The updated model for MACS J0025.4-1222 suggests a substantially smaller critical area than previously estimated. For MACS J0159.8-0849 and Abell 697 we find a single peak and relatively regular morphology, revealing fairly relaxed clusters. Despite being less prominent lenses, three of these clusters seem to have lensing strengths, i.e. cumulative area above certain magnification, similar to the Hubble Frontier Fields clusters (e.g., A($μ>5$) $\sim 1-3$ arcmin$^2$, A($μ>10$) $\sim 0.5-1.5$ arcmin$^2$), which in part can be attributed to their merging configurations. We make our lens models publicly available through the Mikulski Archive for Space Telescopes. Finally, using Gemini-N/GMOS spectroscopic observations we detect a single emission line from a high-redshift $J_{125}\simeq25.7$ galaxy candidate lensed by Abell 697. While we cannot rule out a lower-redshift solution, we interpret the line as Ly$α$ at $z=5.800\pm 0.001$, in agreement with its photometric redshift and dropout nature. Within this scenario we measure a Ly$α$ rest-frame equivalent width of $52\pm22$ Å, and an observed Gaussian width of $117\pm 15$ km/s.

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arXiv2018

GLACiAR, an open-source python tool for simulations of source recovery and completeness in galaxy surveys

The luminosity function is a fundamental observable for characterizing how galaxies form and evolve throughout the cosmic history. One key ingredient to derive this measurement from the number counts in a survey is the characterization of the completeness and redshift selection functions for the observations. In this paper we present GLACiAR, an open python tool available on GitHub to estimate the completeness and selection functions in galaxy surveys. The code is tailored for multiband imaging surveys aimed at searching for high-redshift galaxies through the Lyman Break technique, but it can be applied broadly. The code generates artificial galaxies that follow Sersic profiles with different indexes and with customizable size, redshift and spectral energy distribution properties, adds them to input images, and measures the recovery rate. To illustrate this new software tool, we apply it to quantify the completeness and redshift selection functions for J-dropouts sources (redshift z~10 galaxies) in the Hubble Space Telescope Brightest of Reionizing Galaxies Survey (BoRG). Our comparison with a previous completeness analysis on the same dataset shows overall agreement, but also highlights how different modelling assumptions for artificial sources can impact completeness estimates.

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arXiv2018

RELICS: Strong-lensing analysis of the massive clusters MACS J0308.9+2645 and PLCK G171.9-40.7

Strong gravitational lensing by galaxy clusters has become a powerful tool for probing the high-redshift Universe, magnifying distant and faint background galaxies. Reliable strong lensing (SL) models are crucial for determining the intrinsic properties of distant, magnified sources and for constructing their luminosity function. We present here the first SL analysis of MACS J0308.9+2645 and PLCK G171.9-40.7, two massive galaxy clusters imaged with the Hubble Space Telescope in the framework of the Reionization Lensing Cluster Survey (RELICS). We use the Light-Traces-Mass modeling technique to uncover sets of multiply imaged galaxies and constrain the mass distribution of the clusters. Our SL analysis reveals that both clusters have particularly large Einstein radii ($θ_E>30"$ for a source redshift of $z_s=2$), providing fairly large areas with high magnifications, useful for high-redshift galaxy searches ($\sim2$ arcmin$^{2}$ with $μ>5$ to $\sim1$ arcmin$^{2}$ with $μ>10$, similar to a typical \textit{Hubble Frontier Fields} cluster). We also find that MACS J0308.9+2645 hosts a promising, apparently bright (J$\sim23.2-24.6$ AB), multiply imaged high-redshift candidate at $z\sim6.4$. These images are amongst the brightest high-redshift candidates found in RELICS. Our mass models, including magnification maps, are made publicly available for the community through the Mikulski Archive for Space Telescopes.

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arXiv2018

The Reionization Lensing Cluster Survey (RELICS) and the Brightest High-z Galaxies

Massive foreground galaxy clusters magnify and distort the light of objects behind them, permitting a view into both the extremely distant and intrinsically faint galaxy populations. We present here the z ~ 6 - 8 candidate high-redshift galaxies from the Reionization Lensing Cluster Survey (RELICS), a Hubble and Spitzer Space Telescope survey of 41 massive galaxy clusters spanning an area of ~200 arcmin^2. These clusters were selected to be excellent lenses and we find similar high-redshift sample sizes and magnitude distributions as CLASH. We discover 321 candidate galaxies with photometric redshifts between z ~ 6 to z ~ 8, including extremely bright objects with H-band magnitudes of m_AB ~ 23 mag. As a sample, the observed (lensed) magnitudes of these galaxies are among the brightest known at z> 6, comparable to much wider, blank-field surveys. RELICS demonstrates the efficiency of using strong gravitational lenses to produce high-redshift samples in the epoch of reionization. These brightly observed galaxies are excellent targets for follow-up study with current and future observatories, including the James Webb Space Telescope.

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arXiv2018

RELICS: Strong Lens Models for Five Galaxy Clusters From the Reionization Lensing Cluster Survey

Strong gravitational lensing by galaxy clusters magnifies background galaxies, enhancing our ability to discover statistically significant samples of galaxies at z>6, in order to constrain the high-redshift galaxy luminosity functions. Here, we present the first five lens models out of the Reionization Lensing Cluster Survey (RELICS) Hubble Treasury Program, based on new HST WFC3/IR and ACS imaging of the clusters RXC J0142.9+4438, Abell 2537, Abell 2163, RXC J2211.7-0349, and ACT-CLJ0102-49151. The derived lensing magnification is essential for estimating the intrinsic properties of high-redshift galaxy candidates, and properly accounting for the survey volume. We report on new spectroscopic redshifts of multiply imaged lensed galaxies behind these clusters, which are used as constraints, and detail our strategy to reduce systematic uncertainties due to lack of spectroscopic information. In addition, we quantify the uncertainty on the lensing magnification due to statistical and systematic errors related to the lens modeling process, and find that in all but one cluster, the magnification is constrained to better than 20% in at least 80% of the field of view, including statistical and systematic uncertainties. The five clusters presented in this paper span the range of masses and redshifts of the clusters in the RELICS program. We find that they exhibit similar strong lensing efficiencies to the clusters targeted by the Hubble Frontier Fields within the WFC3/IR field of view. Outputs of the lens models are made available to the community through the Mikulski Archive for Space Telescopes

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arXiv2018

Beacons into the Cosmic Dark Ages: Boosted transmission of Ly$α$ from UV bright galaxies at $z \gtrsim 7$

Recent detections of Lyman alpha (Ly$α$) emission from $z>7.5$ galaxies were somewhat unexpected given a dearth of previous non-detections in this era when the intergalactic medium (IGM) is still highly neutral. But these detections were from UV bright galaxies, which preferentially live in overdensities which reionize early, and have significantly Doppler-shifted Ly$α$ line profiles emerging from their interstellar media (ISM), making them less affected by the global IGM state. Using a combination of reionization simulations and empirical ISM models we show, as a result of these two effects, UV bright galaxies in overdensities have $>2\times$ higher transmission through the $z\sim7$ IGM than typical field galaxies, and this boosted transmission is enhanced as the neutral fraction increases. The boosted transmission is not sufficient to explain the observed high Ly$α$ fraction of $M_\mathrm{UV} \lesssim -22$ galaxies (Stark et al. 2017), suggesting Ly$α$ emitted by these galaxies must be stronger than expected due to enhanced production and/or selection effects. Despite the bias of UV bright galaxies to reside in overdensities we show Ly$α$ observations of such galaxies can accurately measure the global neutral hydrogen fraction, particularly when Ly$α$ from UV faint galaxies is extinguished, making them ideal candidates for spectroscopic follow-up into the cosmic Dark Ages.

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arXiv2018

Wandering off the centre: a characterization of the random motion of intermediate-mass black holes in star clusters

Despite recent observational efforts, unequivocal signs for the presence of intermediate-mass black holes (IMBHs) in globular clusters (GCs) have not been found yet. Especially when the presence of IMBHs is constrained through dynamical modeling of stellar kinematics, it is fundamental to account for the displacement that the IMBH might have with respect to the GC centre. In this paper we analyse the IMBH wandering around the stellar density centre using a set of realistic direct N-body simulations of star cluster evolution. Guided by the simulation results, we develop a basic yet accurate model that can be used to estimate the average IMBH radial displacement ($\left $) in terms of structural quantities as the core radius ($r_\mathrm{c}$), mass ($M_\mathrm{c}$), and velocity dispersion ($σ_\mathrm{c}$), in addition to the average stellar mass ($m_\mathrm{c}$) and the IMBH mass ($M_\mathrm{bh}$). The model can be expressed by the equation $\left /r_\mathrm{c}=A(m_\mathrm{c}/M_\mathrm{bh})^α[σ_\mathrm{c}^2r_\mathrm{c}/(GM_\mathrm{c})]^β$, in which the free parameters $A,α,β$ are calculated through comparison with the numerical results on the IMBH displacement. The model is then applied to Galactic GCs, finding that for an IMBH mass equal to 0.1% of the GC mass, the typical expected displacement of a putative IMBH is around $1''$ for most Galactic GCs, but IMBHs can wander to larger angular distances in some objects, including a prediction of a $2.5''$ displacement for NGC 5139 ($ω$ Cen), and $>10''$ for NGC 5053, NGC 6366 and ARP2.

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arXiv2018

The Cosmic Web Around The Brightest Galaxies During The Epoch Of Reionization

The most luminous galaxies at high-redshift are generally considered to be hosted in massive dark-matter halos of comparable number density, hence residing at the center of overdensities/protoclusters. We assess the validity of this assumption by investigating the clustering around the brightest galaxies populating the cosmic web at redshift $z\sim8-9$ through a combination of semi-analytic modeling and Monte Carlo simulations of mock Hubble Space Telescope WFC3 observations. The innovative aspect of our approach is the inclusion of a log-normal scatter parameter $Σ$ in the galaxy luminosity versus halo mass relation, extending to high-$z$ the conditional luminosity function framework extensively used at low redshift. Our analysis shows that the larger the value of $Σ$, the less likely that the brightest source in a given volume is hosted in the most massive halo, and hence the weaker the overdensity of neighbors. We derive a minimum value of $Σ$ as a function of redshift by considering stochasticity in the halo assembly times, which affects galaxy ages and star formation rates in our modeling. We show that $Σ_{min}(z)\sim0.15-0.3$, with $Σ_{min}$ increasing with redshift as a consequence of shorter halo assembly periods at higher redshifts. Current observations ($m_{AB}\sim27$) of the environment of spectroscopically confirmed bright sources at $z>7.5$ do not show strong evidence of clustering and are consistent with our modeling predictions for $Σ\geqΣ_{min}$. Deeper future observations reaching $m_{AB}\sim28.2-29$ would have the opportunity to clearly quantify the clustering strength, and hence to constrain $Σ$, investigating the physical processes that drive star formation in the early Universe.

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arXiv2018

The Universe is Reionizing at z~7: Bayesian Inference of the IGM Neutral Fraction Using Ly$α$ Emission from Galaxies

We present a new flexible Bayesian framework for directly inferring the fraction of neutral hydrogen in the intergalactic medium (IGM) during the Epoch of Reionization (EoR, z~6-10) from detections and non-detections of Lyman Alpha (Ly$α$) emission from Lyman break galaxies (LBGs). Our framework combines sophisticated reionization simulations with empirical models of the interstellar medium (ISM) radiative transfer effects on Ly$α$. We assert that the Ly$α$ line profile emerging from the ISM has an important impact on the resulting transmission of photons through the IGM, and that these line profiles depend on galaxy properties. We model this effect by considering the peak velocity offset of Ly$α$ lines from host galaxies' systemic redshifts, which are empirically correlated with UV luminosity and redshift (or halo mass at fixed redshift). We use our framework on the sample of LBGs presented in Pentericci et al. (2014) and infer a global neutral fraction at z~7 of $\overline{x}_\mathrm{HI} = 0.59_{-0.15}^{+0.11}$, consistent with other robust probes of the EoR and confirming reionization is on-going ~700 Myr after the Big Bang. We show that using the full distribution of Ly$α$ equivalent width detections and upper limits from LBGs places tighter constraints on the evolving IGM than the standard Ly$α$ emitter fraction, and that larger samples are within reach of deep spectroscopic surveys of gravitationally lensed fields and JWST NIRSpec.

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arXiv2018

HST Grism Observations of a Gravitationally Lensed Redshift 10 Galaxy

We present deep spectroscopic observations of a Lyman-break galaxy candidate (hereafter MACS1149-JD) at $z\sim9.5$ with the $\textit{Hubble}$ Space Telescope ($\textit{HST}$) WFC3/IR grisms. The grism observations were taken at 4 distinct position angles, totaling 34 orbits with the G141 grism, although only 19 of the orbits are relatively uncontaminated along the trace of MACS1149-JD. We fit a 3-parameter ($z$, F160W mag, and Ly$α$ equivalent width) Lyman-break galaxy template to the three least contaminated grism position angles using an MCMC approach. The grism data alone are best fit with a redshift of $z_{\mathrm{grism}}=9.53^{+0.39}_{-0.60}$ ($68\%$ confidence), in good agreement with our photometric estimate of $z_{\mathrm{phot}}=9.51^{+0.06}_{-0.12}$ ($68\%$ confidence). Our analysis rules out Lyman-alpha emission from MACS1149-JD above a $3σ$ equivalent width of 21 Å, consistent with a highly neutral IGM. We explore a scenario where the red $\textit{Spitzer}$/IRAC $[3.6] - [4.5]$ color of the galaxy previously pointed out in the literature is due to strong rest-frame optical emission lines from a very young stellar population rather than a 4000 Å break. We find that while this can provide an explanation for the observed IRAC color, it requires a lower redshift ($z\lesssim9.1$), which is less preferred by the $\textit{HST}$ imaging data. The grism data are consistent with both scenarios, indicating that the red IRAC color can still be explained by a 4000 Å break, characteristic of a relatively evolved stellar population. In this interpretation, the photometry indicate that a $340^{+29}_{-35}$ Myr stellar population is already present in this galaxy only $\sim500~\mathrm{Myr}$ after the Big Bang.

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arXiv2018

Globular Cluster Formation and Evolution in the Context of Cosmological Galaxy Assembly: Open Questions

We discuss some of the key open questions regarding the formation and evolution of globular clusters (GCs) during galaxy formation and assembly within a cosmological framework. The current state-of-the-art for both observations and simulations is described, and we briefly mention directions for future research. The oldest GCs have ages $\ge$ 12.5 Gyr and formed around the time of reionisation. Resolved colour-magnitude diagrams of Milky Way GCs and direct imaging of lensed proto-GCs at z $\sim$ 6 with JWST promise further insight. Globular clusters are known to host multiple populations of stars with variations in their chemical abundances. Recently, such multiple populations have been detected in $\sim$2 Gyr old compact, massive star clusters. This suggests a common, single pathway for the formation of GCs at high and low redshift. The shape of the initial mass function for GCs remains unknown, however for massive galaxies a power-law mass function is favoured. Significant progress has been made recently modelling GC formation in the context of galaxy formation, with success in reproducing many of the observed GC-galaxy scaling relations.

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arXiv2018

A Candidate $z\sim10$ Galaxy Strongly Lensed into a Spatially Resolved Arc

The most distant galaxies known are at z~10-11, observed 400-500 Myr after the Big Bang. The few z~10-11 candidates discovered to date have been exceptionally small- barely resolved, if at all, by the Hubble Space Telescope. Here we present the discovery of SPT0615-JD, a fortuitous z~10 (z_phot=9.9+/-0.6) galaxy candidate stretched into an arc over ~2.5" by the effects of strong gravitational lensing. Discovered in the Reionization Lensing Cluster Survey (RELICS) Hubble Treasury program and companion S-RELICS Spitzer program, this candidate has a lensed H-band magnitude of 25.7+/-0.1 AB mag. With a magnification of μ~4-7 estimated from our lens models, the de-lensed intrinsic magnitude is 27.6+/-0.3 AB mag, and the half-light radius is r_e<0.8 kpc, both consistent with other z>9 candidates. The inferred stellar mass (log [M* /M_Sun]=9.7^{+0.7}_{-0.5}) and star formation rate (\log [SFR/M_Sun yr^{-1}]=1.3^{+0.2}_{-0.3}) indicate that this candidate is a typical star-forming galaxy on the z>6 SFR-M* relation. We note that three independent lens models predict two counterimages, at least one of which should be of a similar magnitude to the arc, but these counterimages are not yet detected. Counterimages would not be expected if the arc were at lower redshift. However, the only spectral energy distributions capable of fitting the Hubble and Spitzer photometry well at lower redshifts require unphysical combinations of z~2 galaxy properties. The unprecedented lensed size of this z~10 candidate offers the potential for the James Webb Space Telescope to study the geometric and kinematic properties of a galaxy observed 500 Myr after the Big Bang.

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arXiv2017

Small-scale Intensity Mapping: Extended Ly$α$, H$α$ and Continuum emission as a Probe of Halo Star Formation in High-redshift Galaxies

Lyman alpha halos are observed ubiquitously around star-forming galaxies at high redshift, but their origin is still a matter of debate. We demonstrate that the emission from faint unresolved satellite sources, $M_{\rm UV} \gtrsim -17$, clustered around the central galaxies may play a major role in generating spatially extended Ly$α$, continuum (${\rm UV + VIS}$) and H$α$ halos. We apply the analytic formalism developed in Mas-Ribas & Dijkstra (2016) to model the halos around Lyman Alpha Emitters (LAEs) at $z=3.1$, for several different satellite clustering prescriptions. In general, our UV and Ly$α$ surface brightness profiles match the observations well at $20\lesssim r \lesssim 40$ physical kpc from the centers of LAEs. We discuss how our profiles depend on various model assumptions and how these can be tested and constrained with future H$α$ observations by the James Webb Space Telescope (JWST). Our analysis shows how spatially extended halos constrain (i) the presence of otherwise undetectable satellite sources, (ii) the integrated, volumetric production rates of Ly$α$ and LyC photons, and (iii) their population-averaged escape fractions. These quantities are all directly relevant for understanding galaxy formation and evolution and, for high enough redshifts, cosmic reionization.

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arXiv2017

Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionization

Within one billion years of the Big Bang, intergalactic hydrogen was ionized by sources emitting ultraviolet and higher energy photons. This was the final phenomenon to globally affect all the baryons (visible matter) in the Universe. It is referred to as cosmic reionization and is an integral component of cosmology. It is broadly expected that intrinsically faint galaxies were the primary ionizing sources due to their abundance in this epoch. However, at the highest redshifts ($z>7.5$; lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations to date are intrinsically bright and, therefore, not necessarily representative of the general population. Here, we report the unequivocal spectroscopic detection of a low luminosity galaxy at $z>7.5$. We detected the Lyman-$α$ emission line at $\sim 10504$ Å in two separate observations with MOSFIRE on the Keck I Telescope and independently with the Hubble Space Telescope's slit-less grism spectrograph, implying a source redshift of $z = 7.640 \pm 0.001$. The galaxy is gravitationally magnified by the massive galaxy cluster MACS J1423.8+2404 ($z = 0.545$), with an estimated intrinsic luminosity of $M_{AB} = -19.6 \pm 0.2$ mag and a stellar mass of $M_{\star} = 3.0^{+1.5}_{-0.8} \times 10^8$ solar masses. Both are an order of magnitude lower than the four other Lyman-$α$ emitters currently known at $z > 7.5$, making it probably the most distant representative source of reionization found to date.

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